ON THE BOUNDED CONTROL OF SOME UNSTABLE MECHANICAL SYSTEMS,
Abstract
This dissertation considers the control and controllability of certain mechanical systems which are inherently unstable. A potential area of application is to the control of rocket vehicles in their launch phase. The majority of effort is directed toward synthesizing control laws for bang-bang controllers--those having only two outputs symmetric about zero. Within the general area, two separate investigations are conducted, and for this reason, the report is in two parts. Part 1 considers the synthesis and application of controls for a class of dynamical systems of arbitrarily high order. A slender, flexible missile is describable by the equations of motion of the subject class. Two separate control laws are derived, one a linear and one a nonlinear function of the plant outputs. Part 2 concerns the adaptive control of a specific fourth-order timevarying mechanical system. Again, potential applications include a rocket vehicle--in this case, one whose center of mass or center of aerodynamic pressure is varying with time. Two different adaptive control processes are formulated in response to two separate problem statements. The feasibility of both techniques is indicated by analog computer simulations. The second process, a 'dual-mode' adaptive scheme, is shown to be able to match the perfect controller in maximizing the range of controllable initial conditions, regardless of the value of the single unknown parameter.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1965
- Accession Number
- AD0624618
Entities
People
- John F. Schaefer
Organizations
- Stanford University